The height response of a surface topography instrument (such as a scanning interference microscope) refers to the relationship between the height measured by the instrument and the actual height of a surface being measured. FIG. 1 shows a plot of a height response, showing the measured height on the vertical axis as a function of the actual height (horizontal axis). Ideally, the response is linear and with unit slope across the dynamic range of the instrument—i.e., the measured height is identical to the actual height, less a constant offset. In general, however, the response curve of a commercial instrument is non-linear and is typically characterized by an amplification coefficient and linear deviation (See, e.g., ISO, “WD 25178-600:2014(E): Geometrical product specifications (GPS)—Surface texture: Areal—Part 600: Metrological characteristics for areal-topography measuring methods,” (International Organization for Standardization, Geneva, 2014)). The amplification coefficient refers to the slope of a linear fit to the non-linear response curve and the linear deviation refers to the deviation of the response curve from the linear fit at a given height. These parameters—the amplification coefficient and the linear deviation—may be determined for a particular instrument when calibrating the instrument.
Conventional methods for measuring height response include the use of material measures, the most common of which is a step-height standard (“SHS”), as shown in FIG. 2. Procedures are available to evaluate both the linearity and the amplitude coefficient using such material measures (See, e.g., C. L. Giusca, R. K. Leach and F. Helery, “Calibration of the scales of areal surface topography measuring instruments: part 2. Amplification, linearity and squareness,” Measurement Science and Technology 23 (6), 065005 (2012)).
In many systems, such as coherence scanning interferometry (CSI sometimes known as scanning white light interferometry or SWLI) microscopes, focus sensing and confocal microscopes, the detection of local surface heights or other surface characteristics such as transparent film thickness relies on a scanning mechanism that mechanically displaces the microscope objective with respect to the sample object along the line of sight of the objective. In an interference microscope, this has the effect of scanning the optical path difference or OPD, which can also be achieved by scanning the reference mirror or otherwise adjusting the optical path. In a confocal or comparable focus-based system, the scanning mechanism moves the focus position in a controlled way. For these CSI, confocal and other scanning systems, the height response is directly linked to knowledge of the velocity and uniformity of motion of the scanning mechanism. Determining the rate and linearity of the scan motion is therefore fundamental to the determination of the amplitude coefficient and linear deviation of the height response. In common practice, the scan is assumed to be sufficiently linear by design, and the amplitude coefficient follows from a single SHS measurement.
Proposed alternatives to SHS measurement include the use of a laser interferometer operating in parallel (see, e.g., J. Schmit, M. Krell and E. Novak, “Calibration of high-speed optical profiler,” 5180, 355-364 (2003); P. J. de Groot, X. Colonna de Lega and D. A. Grigg, “Step height measurements using a combination of a laser displacement gage and a broadband interferometric surface profiler,” Proc. SPIE 4778, 127-130 (2002); S. Zhang, M. Kanai, W. Gao and S. Kiyono, “In-situ absolute calibration of interference microscope,” Proc. ASPE, 448-451 (1999)) or through some or all of the same optics (see, e.g., M. Davidson, J. Liesener, P. de Groot, X. Colonna De Lega and L. L. Deck “Scan error correction in low coherence scanning interferometry”, U.S. Pat. No. 8,004,688 (2011)). Alternatively, some methods for calibration of the linearity of interference microscopes propose to use the interferometer itself with a tilted flat so as to allow for single-camera frame determination of phase during a scan (see, e.g., S. Kiyono, W. Gao, S. Zhang and T. Aramaki, “Self-calibration of a scanning white light interference microscope,” Optical Engineering 39 (10), 2720 (2000)). Similar methods provide a way to validate that the amplification coefficient has not changed over time once calibrated using an SHS (see, e.g., S.-W. Kim, M. Kang and S. Lee, “White light phase-shifting interferometry with self-compensation of PZT scanning errors,” Proc. SPIE 3740, 16-19 (1999)).